Question

Hello! Is it possible to get help on this question?

Answer 1

To determine the graph that corresponds to the given inequality, first, let's write the inequality for y:

`2x\le5y-3`

Add 3 to both sides of the expression

`\begin{gathered} 2x+3\le5y-3+3 \\ 2x+3\le5y \end{gathered}`

Divide both sides by 5

`\begin{gathered} (2)/(5)x+(3)/(5)\le(5)/(5)y \\ (2)/(5)x+(3)/(5)\le y \end{gathered}`

The inequality is for the values of y greater than or equal to 2/5x+3/5, which means that in the graph the shaded area will be above the line determined by the equation.

Determine two points of the line to graph it:

-The y-intercept is (0,3/5)

- Use x=5 to determine a second point

`\begin{gathered} (2)/(5)x+(3)/(5)\le y \\ (2)/(5)\cdot5+(3)/(5)\le y \\ 2+(3)/(5)\le y \\ (13)/(5)\le y \end{gathered}`

The second point is (5,13/5)

Plot both points to graph the line. Then shade the area above the line.

The graph that corresponds to the given inequality is the second one.